Halogens still act as weak-field ligands even in the case of square planar $\ce{[PtCl4]^2-}$ complexes. Weak field does not automatically mean high spin and neither does strong field automatically mean low spin.
Whether a complex adopts a high or a low spin state depends on the central metal’s oxidation state, its position in the periodic table, the ligands, whether they are π-acidic, π-basic or π-neutral, whether the bond is predominantly covalent or dative, the distance between the atoms and sometimes even more subtle factors. Indeed, for some metal-ligand combinations both a high and a low spin complex are known and characterised.
One of the very few rather simple rules when it comes to high or low spin is the fact that any transition metal that is not a $\mathrm{3d}$ metal will usually have a low spin state. In very simple terms this is because the orbitals of higher transition metals are more diffuse and therefore able to form bonds which are more covalent; this in turn leads to greater energetic stabilisations and destabilisations. Therefore, ignore the chlorido ligands in your analysis; look solely at platinum and immediately assume low spin.